how long does it take light to travel to earth from sun ? the sun is 9.3 x 10 ^7mi from earth , and the light travels 1.86 x 10^5mi/s

.

Answer:

  34°

Step-by-step explanation:

The law of cosines is good for finding angles when only sides are known. We'll use the conventional sides a, b, c, and angles A, B, C. Yes, we know the problem statement calls the smallest angle "J". We trust you can make the translation.

  a² = b² +c² -2bc·cos(A) . . . . . for sides a, b, c and angle A

Solving for the angle, we get ...

  A = arccos((b² +c² -a²)/(2bc))

Filling in the numbers with "a" being the shortest side, we have ...

  A = arccos((13² +19² -11²)/(2·13·19)) = arccos(409/494)

  A ≈ 34.113°

The smallest angle, ∠J, is about 34°.

Answer:

b

Step-by-step explanation:

the solution to the given IVP is y(t) = e^(2t) - e^t + 7.

What is Laplace Transform?

The Laplace transform is an integral transform that is widely used in mathematics and engineering to solve differential equations. It allows us to convert a function of time, typically denoted as f(t), into a function of a complex variable s, denoted as F(s), where s = σ + jω (σ is the real part and ω is the imaginary part).

To apply the Laplace transform to the initial value problem (IVP) y'' - 3y' + 2y = sin(2t), with initial conditions y'(0) = 4 and y(0) = -1, we follow these steps:

Take the Laplace transform of both sides of the differential equation, utilizing the properties of the Laplace transform.

L{y''} - 3L{y'} + 2L{y} = L{sin(2t)}

The Laplace transform of the derivatives y'' and y' can be expressed as follows:

L{y''} = s²Y(s) - sy(0) - y'(0)

L{y'} = sY(s) - y(0)

Here, Y(s) denotes the Laplace transform of y(t).

Substitute the initial conditions into the Laplace-transformed equation:

s²Y(s) - s(-1) - 4 - 3(sY(s) + 1) + 2Y(s) = L{sin(2t)}

Simplify the equation:

s²Y(s) + s - 4 - 3sY(s) - 3 + 2Y(s) = L{sin(2t)}

Combine like terms:

(s² - 3s + 2)Y(s) + (s - 7) = L{sin(2t)}

Express the Laplace transform of sin(2t):

L{sin(2t)} = 2/(s² + 4)

Rearrange the equation to solve for Y(s):

(Y(s) = (s - 7) / ((s² - 3s + 2))

Apply the inverse Laplace transform to find y(t):

y(t) = L⁻¹{(s - 7) / ((s² - 3s + 2))}

Perform partial fraction decomposition on the right side:

y(t) = L⁻¹{(s - 7) / ((s - 2)(s - 1))}

Using the inverse Laplace transform table or software, we find:

y(t) = e^(2t) - e^t + 7

Therefore, the solution to the given IVP is y(t) = e^(2t) - e^t + 7.

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Answer:

The perimeter is 4√81 = 4 × 9 = 36 meters.

we have the function

f(t)=9500(0.1)^t

this is an exponential function of the form

y=a(b)^x

where

a is the initial value

b is the base of the function

In this problem

b=0.1

the value of b is less than 1

that means

b=1-r

r=1-0.1

r=0.90

the rate of change is 90%

The solution to the given initial value problem is y(t) = (11/5)e^(2t) + (4/5)e^(5t) + (9/25)e^(5t).

The given initial value problem (IVP) can be solved by using the method of undetermined coefficients. First, we find the complementary solution by solving the associated homogeneous equation: y'' - 7y' + 10y = 0. The characteristic equation is r^2 - 7r + 10 = 0, which factors as (r - 2)(r - 5) = 0.

Therefore, the complementary solution is y_c(t) = c1e^(2t) + c2e^(5t), where c1 and c2 are constants. For the particular solution, we assume y_p(t) = Ae^(5t), where A is a constant to be determined. Plugging this into the original equation, we get 20Ae^(5t) - 35Ae^(5t) + 10Ae^(5t) = 9e^(5t). Solving for A, we find A = 9/5. Hence, the particular solution is y_p(t) = (9/5)e^(5t).

Finally, the general solution is y(t) = y_c(t) + y_p(t) = c1e^(2t) + c2e^(5t) + (9/5)e^(5t). Using the initial conditions, we can solve for c1 and c2 to obtain the unique solution.

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Answer:

6

Step-by-step explanation:

√72 = 6√2. If we draw a square and its diagonals, we know from the 45 - 45 - 45 angle theorem that if the side length is 'x', then the diagonal is 'x√2'. So, in this problem, our x is 6.

By organizing countless data points into comprehensible ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an understandable visual. So Histograms based on data on housing, prices and salaries typically are skewed to the right.

A histogram in statistics is a graphic depiction of the data distribution. The histogram is shown as a collection of rectangles that are next to one another, where each bar represents a different type of data.

A branch of mathematics called statistics is used in many different fields. Frequency is the term for how often numbers appear in statistical data; it can be shown as a table and is known as a frequency distribution.

A histogram is a bar graph-like data visualization that groups various class levels into columns along the horizontal x-axis. The numerical count or percentage of occurrences for each column in the data are shown on the vertical y-axis.

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The required function of the line would be y = 2x + 1.

A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis.

The slope-intercept form is one rule to represent linear function rules. f(x)=mx + b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.

According to the given figure,

We clearly see that the coordinates of the y-intercept would be (0, 1).

The value of the x-coordinate is 1 when y-coordinate is 3.

Here the line passes through points (0, 1) and (1, 3).

Let the required linear function would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]

x₁ = 0, y₁ = 1

x₂ = 1, y₂ = 3

⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]

⇒ y - 3 = (2)[x -1]

⇒ y - 3 = 2x - 2

⇒ y = 2x - 2 + 3

⇒ y = 2x + 1

Therefore, the required function of the line would be y = 2x + 1 .

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Answer:

∠ 1 = 23° , ∠ 2 = 157°

Step-by-step explanation:

∠ 1 and 157° are a linear pair and sum to 180° , that is

∠ 1 + 157° = 180° ( subtract 157° from both sides )

∠ 1 = 23°

∠ 2 and 157° are vertically opposite angles and are congruent , then

∠ 2 = 157°

The total number of sweets given to Mohamed in the beginning is equals to 20.

As given in the question,

Let x be the total number sweets given to Mohamed in the beginning.

Number of sweets he ate when feeling sick = \(\frac{x}{5}\)  

Number of sweets left = x - (x /5)

                                   = (4x / 5)

Number of sweets he ate next day = \(\frac{1}{4}\) × \(\frac{4x}{5}\)

                                                      = x /5

Number of sweets left  = (4x/5) - (x/5)

                                    = (3x /5)

Number of sweets he ate on the following day = \(\frac{1}{4}\) ×\(\frac{3x}{5}\)

                                                                         = (3x / 20)

Number of sweets left at the end = (3x /5) - (3x/20)

                                                   = (12x-3x) / 20

                                                   = (9x /20)

As per given condition,

(9x / 20) = 9

⇒ x = (9 × 20)/9

⇒ x= 20

Therefore, the total number of sweets given to Mohamed in the beginning is equals to 20.

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Answer:

59

Step-by-step explanation:

Answer:

1. 5xy^3

2.  4/9m^6 n^4

3. 2a^2/c

4. 4x^3m+6/3

Step-by-step explanation:

The proportion of all bearings falls in the acceptable range is 0.9544 (rounded to four decimal places).

The proportion of all bearings falls in the acceptable range is 0.9544. The given problem statement asks to determine the proportion of bearings produced in the acceptable range, given the mean, standard deviation and the acceptable range for bearing diameters.Solution: The given distribution is normal with mean (μ) = 1.5 cm and standard deviation (σ) = 0.02 cm. Also, the acceptable range of diameter is from 1.46 cm to 1.54 cm, hence the distance between the lower limit and mean is: $Z_{lower}=\frac{1.46-1.5}{0.02}=-2$Similarly, the distance between upper limit and mean is:$Z_{upper}=\frac{1.54-1.5}{0.02}=2$Using the standard normal table or calculator, we can obtain the probability (proportion) of the distribution that falls within the acceptable range (from $Z_{lower}$ to $Z_{upper}$).So, the proportion of all bearings that fall in the acceptable range is:$$P(-2≤Z≤2)=0.9544$$Therefore, the proportion of all bearings falls in the acceptable range is 0.9544 (rounded to four decimal places).

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Answer: The length of a side of the square is given by x

The length of a side of the equilateral triangle is given by x=1

Given is : The perimeter of a square is equal to the perimeter of an equilateral triangle.

Perimeter of square is given as 4 x side.

Perimeter of equilateral triangle is given as 3 x side.

So, we will make both equal.

As x = 1 for triangle, the equation becomes:

4x=3

so x=3/4

Step-by-step explanation:

Answer: A

Step-by-step explanation:

The two numbers required to solve the following problem are, 13.3 and 6.7

What is Derivative?

The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.

Solution:

Let the ture positive numbers be x,(x,y>0)

x + y = 20 -------- Given

We need to maximise \(xy^{2}\)

x = 20 - y

f(y) = (20 - y)*\(y^{2}\)

f(y) = 20\(y^{2}\) - \(y^{3}\)

f'(y) = 0

On differentiating:

f'(y) = 40y - 3\(y^{2}\)

0 = 40 - 3y

y = 13.3

x = 6.7

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Answer:

x = 24

Step-by-step explanation:

Step 1 - get 'x' by itself

5x + 5 = 4x + 29

-4x   -5   -4x   -5

Step 2 - solve

x = 24

Check

5(24)+5 = 125

4(24)+29 = 125

Answer:

X=25

Step-by-step explanation:

5x+5=4x+29

-5 -4x

1x=25

The options are not provided, but method is stated below

Answer:

Quadratic equation ax2 - 6x + c = 0

options would be given for a and c

These conditions will fetch us the result required among the options.

Note : the \(\geq\) sign will give us the result for Two real unequal solutions and two real equal solutions.  If we only need Real unequal solutions we only use > sign instead of \(\geq\)

Answer:

Picture is not clear please post a clear picture. Note brainly is meant to be one question per post for further reference

Answer:

7:47

Step-by-step explanation:

Here are two ways of solving this:

The video will be half the time of 15:34, so you need to divide the time 15:34 by 2.

Method 1)

Use the tip. The video is 15 minutes and 34 seconds long.

Convert minutes to seconds: 15 * 60 = 900

Add 34 seconds to the 15 minutes: 900 seconds + 34 seconds = 934 seconds

The video is 934 seconds long.

Divide the total seconds by 2: 934/2 = 467

467 seconds = 420 seconds + 47 seconds = 7 minutes and 47 seconds

Answer: 7:47

Method 2)

Divide the minutes by 2 and divide the seconds by 2.

15 minutes and 34 seconds.

Divide minutes by 2: 15/2 = 7.5

Divide seconds by 2: 34/2 = 17

Now we need to add 7.5 minutes and 34 seconds.

0.5 minutes is half a minute, so it's 30 seconds.

7.5 minutes + 17 seconds =

= 7 minutes + 0.5 minute + 17 seconds

= 7 minutes + 30 seconds + 17 seconds

= 7 minutes + 47 seconds

= 7:47

Answer: 7:47

Answer:

8a-9=7a+1 (inscribed angle are equal standing on the arc)

8a-7a=1+9

a=10

Step 1:

50%= 50/100 = 0.5

Step 2:

50% of 50%= (50×0.5)/100= 0.25

Step 3:

50% of 50% of 50% = (50×0.25)/100= 0.125

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Answer:

A. 16 to 20 is equivalent to ratio 32:40

Answer:

the answer is D

Step-by-step explanation:

y=\(x^{2}\)+1

Answer:

Step-by-step explanation:

20

Answer: KL IS 3 + 9 THEN 5 MINUS NINE

Step-by-step explanation: FIND KL

The worst-case running time of the given function is O(n^2). We can choose any positive value for c, and there is no specific value for n0 since the inequality holds true for all n ≥ n0.

To determine the worst-case running time of a function and express it in big-O notation, we need to count the number of primitive operations and find the dominant term that grows the fastest as the input size increases. Let's analyze the function and find its worst-case running time.

def exampleFunction(n):

   for i in range(n):

       for j in range(n):

           print("Operation")

The given function consists of two nested loops, where both loops iterate from 0 to n-1. Inside the inner loop, there is a single primitive operation, which is printing the string "Operation." Let's break down the number of operations and find the worst-case running time.

The outer loop executes n times, and for each iteration of the outer loop, the inner loop executes n times. Therefore, the total number of operations can be calculated as follows:

1 operation (print statement) * n^2 (number of iterations of both loops)

Hence, the worst-case running time of the function can be expressed as O(n^2), indicating that it grows quadratically with the input size.

To find the values for c and n0, let's recall the definition of big-O notation. A function f(n) is said to be O(g(n)) if there exist positive constants c and n0 such that f(n) ≤ c * g(n) for all n ≥ n0.

In our case, the worst-case running time of the function is O(n^2). To find suitable values for c and n0, we need to demonstrate that the number of operations is bounded by c * n^2 for sufficiently large values of n.

Since the constant factor c can vary, we can choose any positive value for c. Let's consider c = 1 for simplicity.

Now, we need to find n0, the point at which the inequality f(n) ≤ c * g(n) holds true. In this case, it means finding the value of n from which the number of operations is always less than or equal to n^2.

By observing the function, we can see that for any value of n, the number of operations is equal to n^2. Therefore, we can choose any positive value for n0 since the inequality holds true for all n ≥ n0.

In summary, the worst-case running time of the given function is O(n^2). We can choose any positive value for c, and there is no specific value for n0 since the inequality holds true for all n ≥ n0.

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If the margin of error for a 95% confidence interval for a population parameter equals 0.13, it means that we can be 95% confident that the true value of the population parameter lies within a range that extends 0.13 units in either direction from the point estimate.

A confidence interval is a range of values within which we estimate the true value of a population parameter with a certain level of confidence. The margin of error is the amount by which the estimate is likely to deviate from the true population value. In this case, the margin of error is 0.13.

A 95% confidence interval means that if we were to take multiple samples from the same population and construct confidence intervals for each sample using the same method, 95% of those intervals would contain the true population parameter. In other words, there is a 95% chance that the true value of the population parameter falls within the calculated confidence interval.

The margin of error of 0.13 indicates the width of the confidence interval. It represents the maximum amount by which the point estimate, which is the center of the confidence interval, can deviate from the true population value. The confidence interval will extend 0.13 units in both directions from the point estimate.

Therefore, if the margin of error for a 95% confidence interval for a population parameter equals 0.13, it means that we can be 95% confident that the true value of the population parameter lies within a range that extends 0.13 units in either direction from the point estimate

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Answer:

Step-by-step explanation:

The sides of a triangle measure 6, 8 and 10 cm. What is the area of the triangle?

from the data it is a right triangle, 10 cm is the hypotenuse

so

1/2 (6 * 8) =

1/2 * 48 =

24 units²